Apparatus for tracking the fundamental frequency of a signal with harmonic components stronger than the fundamental

ABSTRACT

Methods and digital circuits providing frequency correction to frequency synthesizers are disclosed. An FLL digital circuit is provided that is configured to handle a reference frequency that is dynamic and ranges over a multi-decade range of frequencies. The FLL circuit includes a digital frequency iteration engine that allows for detection of disappearance of a reference frequency. When the digital frequency iteration engine detects that the reference frequency signal is not available, the oscillator generated frequency is not corrected, and the last value of the oscillator generated frequency is held until the reference frequency signal becomes available again. This FLL circuit is also preceded by a low-pass filter which is dynamically tuned to the frequency to which the FLL locks, eliminating harmonic components in the original signal which might otherwise cause errors in frequency estimation.

CROSS REFERENCE TO RELATED U.S. PATENT APPLICATIONS

The present application is related to U.S. patent application entitledSYNCHRONOUS SAMPLING OF ANALOG SIGNALS, filed Sep. 25, 2015, Ser. No.14/864,899, which is incorporated herein by reference in its entiretyfor all purposes.

The present application is also related to U.S. patent applicationentitled FAST-LOCKING FREQUENCY SYNTHESIZER, filed Sep. 25, 2015, Ser.No. 14/864,886.

BACKGROUND

The present disclosure relates generally to frequency synthesizers.Frequency synthesizers generate frequencies from one or more fixedreference frequencies, and are found in various devices includingmusical instruments, GPS systems, mobile telephones, etc.

There are several different types of frequency synthesizers includingdirect analog synthesizers, direct digital synthesizers, and indirectdigital synthesizers. The indirect digital synthesizers based onphase-locked loops (“PLLs”) are compatible with integrated circuittechnology. The indirect digital PLL synthesizers often include thefollowing components: voltage controlled oscillators, mixers, PLLs,frequency multipliers, and frequency dividers. A voltage-controlledoscillator of a PLL synthesizer typically generates an output frequencyfrom the filtered output of the phase frequency detector. A divider thenscales the output frequency. In some applications, a reference frequencyis dynamic and can span a multi-decade range of frequency values. Inthese cases, the traditional PLL synthesizers have drawbacks.

SUMMARY

Implementations of the methods, frequency-locked loop circuits, andfrequency synthesizers for providing correction to frequencies aredisclosed herein. One implementation is a method for correctingfrequencies. The method includes receiving a first frequency generatedby an oscillator. The method further includes receiving a referencefrequency. The method further includes determining a number of firstfrequency cycles in one reference frequency cycle. The method furtherincludes receiving a dropout value associated with the referencefrequency. The method further includes determining a second frequencybased on a predetermined frequency factor, the dropout value, thedetermined number of first frequency cycles, the first frequency, andthe reference frequency. The predetermined frequency factor providestarget relationship between the first frequency and the referencefrequency.

Another implementation is a frequency-locked loop circuit. Thefrequency-locked loop circuit includes a digitally controlled oscillatorconfigured to generate a first frequency. The frequency-locked loopcircuit further includes a dropout detector configured to receive areference frequency, and generate a dropout value. The frequency-lockedloop circuit further includes a digital frequency iteration engine. Thedigital frequency iteration engine includes a first circuit configuredto receive the first frequency and the reference frequency, and generatea number of first frequency cycles in one reference frequency cycle. Thedigital frequency iteration engine further includes a second circuitconfigured to receive the number of first frequency cycles, and generatea second frequency based on a predetermined frequency factor, thedropout value, the determined number of first frequency cycles, thefirst frequency, and the reference frequency. The predeterminedfrequency factor provides a target relationship between the firstfrequency and the reference frequency.

Another implementation is a frequency synthesizer. The frequencysynthesizer includes a frequency-locked loop circuit. Thefrequency-locked loop circuit includes a digitally controlled oscillatorconfigured to generate a first frequency. The frequency-locked loopcircuit further includes a dropout detector configured to receive areference frequency and a first frequency, and generate a dropout value.The frequency-locked loop circuit further includes a digital frequencyiteration engine. The digital frequency iteration engine includes afirst circuit comprising a Gray-code counter, a Gray-to-binaryconverter, a first plurality of flip-flops. The first circuit isconfigured to receive the first frequency and a reference frequency, andgenerate a number of first frequency cycles in one reference frequencycycle. The digital frequency iteration engine further includes a secondcircuit comprising a multiplexor, a second plurality of flip-flops, andan estimation module. The second circuit configured to receive thenumber of first frequency cycles, and generate a second frequency basedon a predetermined frequency factor, the dropout value, the determinednumber of first frequency cycles, the first frequency, and the referencefrequency. The predetermined frequency factor provides a targetrelationship between the first frequency and the reference frequency.

Another implementation is of a self-tuning low-pass filter whichisolates the fundamental frequency in a music signal to avoid false zerocrossings and the errors in frequency tracking caused as a result aredisclosed herein.

These implementations are mentioned not to limit or define the scope ofthe disclosure, but to provide an example of an implementation of thedisclosure to aid in understanding thereof. Particular implementationsmay be developed to realize one or more of the following advantages.

BRIEF DESCRIPTION OF THE DRAWINGS

The details of one or more implementations are set forth in theaccompanying drawings and the description below. Other features,aspects, and advantages of the disclosure will become apparent from thedescription, the drawings, and the claims, in which:

FIG. 1 is a block diagram of a frequency-locked loop system, in anaccordance with a described implementation;

FIG. 2 is a diagram of a digitally controlled oscillator, in anaccordance with a described implementation;

FIG. 3 is a block diagram of a digital frequency iteration engine, in anaccordance with a described implementation;

FIG. 4 is an illustration of log₂ approximation, in an accordance with adescribed implementation;

FIG. 5 is a diagram of an output divider, in an accordance with adescribed implementation;

FIG. 6A illustrates a digital circuit schematic of a dropout detector,in an accordance with a described implementation;

FIG. 6B illustrates a state table and a timing diagram associated withthe dropout detector, in an accordance with a described implementation;and

FIG. 7 is a flow diagram of a process for determining a frequency, inaccordance with a described implementation.

FIG. 8 is a block diagram of a frequency-locked loop system withself-tuned input filter to remove harmonics present in the input signal,in an accordance with a described implementation;

FIG. 9 is one embodiment of an voltage-controlled filter withexponential relationship between input voltage and filter cutofffrequency;

FIG. 10 is the magnitude transfer function of a proposed low-pass filterwith high frequency shelf;

FIG. 11 is the group delay of a proposed low-pass filter with highfrequency shelf;

FIG. 12 contains a simplified block diagram and difference equation andz-domain analysis for evaluating stability of the tracking filterfeedback loop.

Like reference numbers and designations in the various drawings indicatelike elements.

DETAILED DESCRIPTION

Numerous specific details may be set forth below to provide a thoroughunderstanding of concepts underlying the described implementations. Itmay be apparent, however, to one skilled in the art that the describedimplementations may be practiced without some or all of these specificdetails. In other instances, some process steps have not been describedin detail in order to avoid unnecessarily obscuring the underlyingconcept.

In certain disciplines such as electronic music, a frequency may bedesired that exhibits a certain ratio relationship to another frequencysuch as a reference frequency. Aesthetically pleasing results can beobtained if the generated frequency corresponds to a rational multipleR=N/D of the reference frequency, where N (the numerator) and D (thedenominator) are both integers. Such a configuration may be used in manyother disciplines (e.g., data communication systems, etc.) other thanelectronic music and the embodiments disclosed herein are in no wayintended to be restricted to the realm of electronic music.

In any discipline where the reference frequency is dynamic (i.e.,changing in time) and can span over a multi-decade range, traditionalphase-locked loop (“PLL”) systems have many drawbacks. The multi-decaderange of the reference frequency may mean several decades, or factors of10. Electronic music is an example discipline for which the referencefrequency is dynamic and spans a multi-decade range.

As used herein, “phase-locked” refers to a PLL system forcing theinstantaneous phase of the output signal to “line up” with theinstantaneous phase of the input signal. While second-order PLLs havesome desirable noise properties, they may function by integrating thephase error between the reference signal and the feedback signal fromone reference cycle to the next and adjusting the frequency of theoutput signal until the phase error is driven to zero. If there is anextremely large phase error at any time, it may take the second-orderPLL an especially long time to lock or it may “slew” or behavenon-linearly during locking. Thus, the second-order PLLs can also beproblematic in applications where the reference frequency changesdynamically and over a multi-decade frequency range.

Although these effects (e.g., the “locking” effect) can be exploited asa pleasing side-effect in electronic music, it may be desirable tomitigate these effects and thereby minimize the locking time. In thecontext of electronic music, latency may be important for effects, whichmust function in real-time. The reference signal and the oscillatorgenerated signal may operate at different frequencies, and in particularin electronic music, the frequency relationships are not expressed interms of a “relative phase” between the two signals, but rather asharmonies or dissonances.

When the “locking” of a synthesized frequency to another frequency isnot meant to be experienced as an additional effect, but rather is meantto be imperceptibly fast, traditional PLLs do not satisfy this need.Another drawback of traditional frequency synthesizers (both PLLs andFLLs) is that if the reference signal disappears, the synthesizer outputmay not necessarily behave “well” as the frequency could drift to themaximum frequency or minimum frequency allowed by the system.

According to various implementations disclosed herein, afrequency-locked loop (“FLL”) system is provided. The FLL systemutilizes a digital, rather than analog approach, and the FLL system doesnot perform phase locking. In some embodiments, the FLL system isconfigured to detect when the reference signal has disappeared. When theFLL system detects that the reference signal disappeared, it may suspendthe loop operation and “hold” the current digital frequency “code”.

Referring to FIG. 1, a block diagram of a FLL system 100, in accordancewith a described implementation, is shown. The block diagram of thefrequency-locked loop system 100 illustrates the schematic of theoverall architecture of the digital FLL circuit. As shown, thefrequency-locked loop system 100 includes a dropout detector 104, adigital frequency iteration engine 106, a 22-bit counter 108, adigitally controlled oscillator (“DCO”) 110, a sigma-delta modulator112, and an output divider 114. In some implementations, thesecomponents may be integrated into a chip (e.g., used in a musicsynthesizer). The FLL system 100 may include additional components thatare not displayed in FIG. 1.

The dropout detector 104, the digital frequency iteration engine 106,and the 22-bit counter 108, each receive a reference signal 102. Thereference signal 102 may be generated by an oscillator that is notillustrated in FIG. 1 (e.g., an oscillator distinct from the DCO 110).The frequency of the reference signal 102 may be dynamic and may changeover a multi-decade frequency range.

The DCO 110 generates a DCO output signal 124, which is transmitted tothe output divider 114, the sigma-delta modulator 112, and the 22-bitcounter 108. One implementation of the DCO 110 is illustrated in FIG. 2.However, the DCO 110 may be designed in any other manner, and FIG. 2provides one implementation.

The 22-bit counter 108 measures elapsed time by counting cycles of thedigitally controlled oscillator 110. The output 128 of the 22-bitcounter 108 is sent to the digital frequency iteration engine 106, whichuses the output 128 to generate an estimate of the frequency. Thedigital frequency iteration engine 106 makes corrections that then goback to the digitally controlled oscillator 110 to change its frequency124, so that it reaches a predetermined target.

The sigma-delta modulator 112 is a digital signal modulator thatreceives 8-bit digital output 132, representing the fractional part ofthe desired DCO frequency, from the digital frequency iteration engine106, and the DCO output 124 from the DCO 110. The sigma-delta modulator112 is a state machine that changes state on every DCO clock cycle, andproduces a 2-bit output 134 that is transmitted to an adder block 122.

The output divider 114 receives the DCO output 124 and the output 130,and generates CK75 signal 120, SCK signal 116, and AUD signal 118. TheCK75 signal 120 is passed to the dropout detector 104, which alsoreceives the reference frequency 102 as input. The dropout detector 104determines whether the reference frequency 102 has dropped out. Theoutput 126 of the dropout detector 104 is sent to the digital frequencyiteration engine 106.

The adder block 122 adds the 8-bit output 130, representing the integerpart of the desired DCO frequency and generated by the digital frequencyiteration engine 106, to the 2-bit output 134 of the sigma-deltamodulator 112, generating an 8-bit output 136 that is transmitted to thedigitally controlled oscillator 110.

In other implementations, a digital FLL or PLL system can be designedusing another method. For example, a linear feedback loop may beutilized, which may have a different settling behavior than thelogarithmic loop utilized herein.

FIG. 2 illustrates an exemplary schematic of the DCO 110, in accordancewith one implementation. The DCO 110 receives digital input. In someembodiments, in order to achieve a multi-decade frequency range, aresistor-capacitor (RC) based relaxation oscillator may be utilized,where the resistor is tuned digitally over an eight-octave range (i.e.,a factor of 256). In other embodiments, the FLL system 100 can utilize aDCO with another frequency tracking range. For example, the frequencytracking range can be extended.

As shown in FIG. 2, the DCO 110 includes a digitally-programmableresistor network, a two “bridge” network of four switches each, twocapacitors, two voltage comparators, two reference voltages (which canbe generated by dividing the supply voltage of the DCO usingresistor-based voltage dividers), and digital logic.

A resistor 202 is connected with one terminal grounded, and the otherterminal connected to switches 222 and 224. The second terminal of theswitch 222 is connected to a capacitor 244 at a node “P,” while thesecond terminal of the switch 224 is connected to a capacitor 246 at anode “N.” The switches 220 and 226 are connected between capacitors 244and 246, respectively, and the power supply.

The nodes “P” and “N” are connected via switches 228 and 234,respectively, to the positive and negative inputs of a voltagecomparator 204. Additionally, a reference voltage V1 is connected viaswitches 230 and 232 to the positive and negative inputs, respectively,of the voltage comparator 204. The output of the voltage comparator 204is used to generate two non-overlapping normal and delayed clocks, whichare in turn used to control the eight switches 220 through 234. In someembodiments, the voltage comparator 204 can be designed to include oneor more resistors, and an operational amplifier.

In some embodiments, the RC-based relaxation oscillator 110 has twophases of operation: a first phase and a second phase. During the firstphase of operation of the DCO 110, the switches 222 and 226 are closedand the switches 220 and 224 are opened. The capacitor 246 is shortedout to the supply and the programmable resistor 202 proceeds todischarge the capacitor 244 from the supply towards ground. Voltage “P”during this phase exhibits the decaying exponential shape with timeconstant (resistor 202)*(capacitor 244). The switch 228 connects thenode “P” to the positive comparator input and the switch 232 connectsthe reference voltage V1 to the negative comparator output. Thecomparator output remains high until the voltage at node “P” crosses thereference voltage V1 in the negative-going direction. At this point, thecomparator output is driven low, and the operation of the DCO 110transfers to the second phase.

During the second phase, the switches 222 and 226 are opened and theswitches 220 and 224 are closed. Voltage “N” starts out at the supplyand decays towards ground with time constant (resistor 202)*(capacitor246) via the resistor 202, the capacitor 246, and the switch 222. Thecapacitor 244 is shorted out to the supply to prepare for the next firstphase. The switches 228 through 234 also reverse roles and thecomparator changes state again when voltage “N” crosses the referencevoltage V1. As a result, a relaxation oscillator is achieved with period(resistor 202)*(capacitor 244)+(resistor 202)*(capacitor 246). In someembodiments, the capacitors 244 and 246 may be identical so that the twophases will last equally long.

A voltage comparator 206 and an XOR gate 218 may be utilized to “double”the DCO 110 frequency. The decaying exponential waveforms at nodes “P”and “N” are compared via the voltage comparator 206 to a secondreference voltage V2 (which may be appropriately chosen but necessarilyhigher than V1) through a bridge switch network composed of the switches236-242, which functions the same way as the bridge switch networkcomposed of the switches 228-234. The logic gates 208-216 after thevoltage comparator 204 ensure that the switch control signals 248 and250 are non-overlapping.

In some embodiments, the resistor 202 may be controlled by 8 bits. Inother embodiments, the resistor 202 may be controlled by another numberof bits (e.g., 16 bits). The resistor 202 may have an inverseexponential characteristic with respect to the 8-bit control word, whichcan be expressed by the following formula: R=R0*2^(−D/32) (referred toas “Equation 1” herein), where R0 is the maximum resistance(corresponding to minimum DCO operating frequency) and D is the 8-bitDCO control word. According to this formula, the DCO has 32 steps peroctave and may cover 8 octaves over its entire range using an 8-bitcontrol word (5 bits per octave with 3 MSBs to cover 8 octaves).

The resistor 202 can be constructed in many ways. In one embodiment,unit resistor cells may be used in series and parallel combinations togive incremental conductances on each code step which yield thecharacteristic in Equation 1.

The inverse exponential characteristic of the resistor 202 may yield anexponential characteristic for the DCO frequency 124 itself. Assumingthat the capacitance of the capacitor 244 equals the capacitance of thecapacitor 246 and ignoring comparator delay, the DCO frequency can beexpressed as follows: Fdco=Fmin*2^(D/32) (referred to as “Equation 2”herein), where Fmin is the minimum DCO frequency and D is the 8-bit DCOcontrol word.

While FIG. 2 illustrates one way of designing the DCO 110, the DCO 110can be designed in another manner and the FLL system 100 is not limitedto the embodiment shown in FIG. 2.

FIG. 3 illustrates a block diagram of the digital “frequency-iteration”engine 106. The digital frequency iteration engine 106 generates a16-bit frequency 344, of which the 8 most significant bits represent theinteger part of the desired frequency control word and the 8 leastsignificant bits represent the fractional part, using the DCO output 124received from the DCO 110 and the reference frequency 102. In someembodiments, the digital frequency iteration engine 106 may depend on arelationship between the frequency 124 generated by the DCO 110 and thereference frequency 102.

As shown, the digital frequency iteration engine 106 includes a bank offlip-fops 306, 318, 320, 322, 324, and 336, a Gray to binary converter310, a subtractor block 314, a multiplexor 328, an estimator block 330,and a subtractor block 334. In other embodiments, the digital frequencyiteration engine 106 may include other components (e.g., flip-flops,counters, multiplexors, adders, subtractors, etc.). In otherembodiments, the digital frequency iteration engine 106 may include asubset of the components displayed in FIG. 3.

In some embodiments, the 22-bit Gray-code counter 108, the D flip-flops306, the Gray to binary converter 310, and a differentiator, composed ofthe D flip-flops 318, and the subtractor block 314, measure the numberof digitally controlled oscillator 110 cycles that occur betweensuccessive reference clock edges. Therefore, the output 326 provides ameasurement of the frequency error between the DCO output 124 and thereference frequency 102.

The 22-bit Gray-code counter 108 receives the DCO output 124 generatedby the digitally controlled oscillator 110. In some embodiments, the22-bit Gray-code counter 108 counts on the edges of the DCO output 124clock. The 22-bit Gray-code counter 108 saves the count as a 22-bitstate.

The 22-bit Gray-code counter 108 is a Gray-code counter, with one bitchanging on each state transition. In some embodiments, the 22-bitGray-code counter 108 may be implemented as a component of the digitalfrequency iteration engine 106. In these embodiments, FIG. 1 would notinclude the 22-bit Gray-code counter 108, and the digital frequencyiteration engine 106 would receive the DCO output 124.

As the reference clock is asynchronous with the DCO clock, theillustrated Gray-code embodiment of the free-running counter 108 mayreliably latch the state of the 22-bit counter 108. Although atraditional binary counter may be utilized, the traditional binarycounter may not be able to reliably latch the state of the counter.

The 22-bit output 128 generated by the 22-bit Gray-code counter 108 isreceived as input by the bank of flip-flops 306. As shown, the referencefrequency 102 is the clock for the flip-flops 306. The input into thebank of flip-flops 306 changes on every cycle of the digitallycontrolled oscillator 110. The bank of flip-flops 306 takes a snapshotof the 22-bit word 128 on every edge of the reference frequency 102.

As shown, the output 128 of the Gray-code counter 108 is 22 bits, whichis latched with the bank of 22 D flip-flops 306. In other embodiments,the Gray-code counter 108 may produce an output having another number ofbits (e.g., 16 bits, 32 bits, etc.), in which case, the bank offlip-flops 306 would have a corresponding number of flip-flops. Forexample, the Gray-code counter 108 may produce an output 128 having 16bits, and the bank of flip-flops 306 would have 16 flip-flops to latchthe counter state. In another example, the Gray-code counter 108 mayproduce an output 128 having 32 bits, in which case the bank offlip-flops 306 would have 32 flip-flops to latch the counter state.

The Gray to binary converter 310 receives the 22-bit Gray-code word 308from the bank of flip-flops 306, and converts the 22-bit Gray-code word308 to the equivalent 22-bit binary value 312. The 22-bit binary output312 of the Gray to binary converter 310 provides a measurement of thetime, thereby providing a number of DCO 110 cycles that have elapsed.

The bank of flip-flops 318 receives the 22-bit binary output 312 asinput, and the reference frequency 102 is the clock. The bank offlips-flops 318 includes 22 D flip-flops. The bank of flip-flops 318takes a snapshot of the 22-bit word 312 on every edge of the referencefrequency 102. As a result, the bank of flip-flops 318 provides a delayby another cycle of the reference frequency 102.

The number of flip-flops in the bank 318 may correspond to the number ofbits in the computation (i.e., in this case, 22 flips-flops in the bankof flips-flops 318). In other embodiments, the system can be designedwith fewer or more bits, which would be directly reflected in the numberof flip-flops in the bank of flip-flops 318. For example, the output 128of Gray-code counter 108 may be 16 bits, in which case the output 312 ofthe Gray-to-binary converter counter 108 may be 16 bits, and the bank offlip-flops 318 would include 16 flip-flops. In another example, theoutput 128 of Gray-code counter 108 may be 32 bits, in which case theoutput 312 of the Gray-to-binary converter counter 108 may be 32 bits,and the bank of flip-flops 318 would include 32 flip-flops.

The subtractor block 314 receives the current value of the count 312 andthe last value of the count 316 when the last reference frequency 102edge occurred. The subtractor block 314 determines the differencebetween the values 312 and 316. The difference between the values 312and 316 is an output 326, which is a measurement of a number of DCOcycles in one reference frequency cycle (i.e., between two referencefrequency edges). In some embodiments, the target may be to make thatnumber a certain predetermined number. The rest of the block diagramshown in FIG. 3 illustrates reaching that target.

As shown in FIG. 3, the predetermined target number is set to 8,192. Insome embodiments, musical sources are used for the reference frequency.For example, the range of the piano keyboard can be utilized as a targetfor the frequency tracking range. The frequencies of the standard pianokeyboard may range from 27.5 Hz to 4,186 Hz. 8,192 times 27.5 Hz equals225.28 kHz. The DCO output 124 is divided by a power of two, which is atleast 2 to generate a sample clock for the audio signal. As a result,225.28 kHz divided by 2 produces 112.64 kHz. The synchronous samplingfrequency may be between 100 kHz and 200 kHz, and 112.64 kHz is withinthat range. 8,192 is a power of two (i.e., 2^13), which is convenient towork with in digital circuits. On the high end, 8,192 times 4,186 Hzequals 34.29 MHz. It may be challenging to design the DCO 110 to runhigher than about 40 MHz without having to account for the comparatordelay. The equation used herein for the DCO frequency versus theresistor code assumes ignoring comparator delay, which is possible whenthe period of oscillation is large compared to the comparator delay(i.e., when the frequency of oscillation is “low,” which for thisoscillator means less than 40 MHz). Accordingly, the target number of8,192 is one implementation for the design of the digital frequencyiteration engine 106 illustrated in FIG. 3.

Although the predetermined target number utilized in FIG. 3 is 8,192,another number may be used as the target. It may be desirable to set themultiplication factor to a high value, since generating a higherfrequency and dividing it down may result in a “cleaner” signal (i.e.,less timing jitter) than generating the lower-frequency signal directly.

The digital “frequency-iteration” engine 106 further includes a“dropout” control multiplexer 328, a base-2 log estimator 330, asubtractor block 334, and flip-flops 336. The base-2 log estimator 330is a piecewise-linear logarithm calculation circuit, which estimates thevalue of 16 log₂(N/8192). The subtractor block 334 subtracts the output332 of the logarithm estimator block 330 from the current digitalfrequency code 338, latched in D flip-flops 336. As a result, a newfrequency code 344 is generated.

The flip-flops 320, 322, and 324 delay the positive edge of thereference clock 102 by up to three DCO cycles and use this delayedreference clock edge to latch the new 16-bit frequency word 344. In someembodiments, three DCO cycles may be used as this number of DCO cyclesmay provide all the digital circuits between the 22-bit Gray-codecounter 108 and the frequency word flip-flops 336 time to settlecompletely, so there would be no errors in the latching of the 16-bitfrequency word. Usage of three DCO cycles may be specific to thefabrication process selected for the design (e.g., 0.35 um). In otherembodiments, another number of DCO cycles (e.g., two DCO cycles, one DCOcycle, etc.) may be utilized (e.g., with other processes that may allowfor a shorter delay).

The multiplexor 328 is a 2-to-1 multiplexor that receives two inputs:the subtractor output 326 and an input 340. As shown in FIG. 3, theinput 340 has a value of 8,192. The selector input for the multiplexor328 is a dropout 126, which is received from the dropout detector 104.In some embodiments, the dropout 126 having a value of “1” may indicatethat there is no signal, in which case the output 346 of the multiplexor328 would have a value of 8,192. As a result, the base-2 log estimatorblock 330 would receive an input value of 8,192. In this instance,passing the value of 8,192 to the base-2 log estimator block 330 causesthe circuit 300 to determine that the DCO 110 is perfectly locked sincethe value 8,192 is the target for that other input into the multiplexor228. Thus, if there is no signal, the current value of the DCO frequencyis maintained. As a result, the circuit 100 is locked, and nocorrections are made to the DCO frequency.

If there is a reference frequency signal and the dropout 126 is low, theoutput 326 of the subtractor 314 is passed to the estimator block 330.The estimator block 330 estimates 16 log₂(in/8192), where “in” is theoutput 346 of the multiplexor 328. When the input (i.e., the output 346)to the estimator block 330 equals 8,192, the log is zero, in which casethe DCO frequency doesn't get changed. The estimator 330 can perform(in/8192) calculation using digital shift operation (i.e., because 8192is power of 2, the decimal point is moved in the binary number). Thebase-2 log estimator block 330 provides an estimate 332 by calculatinglog₂. This estimate 332 may be not an exact calculation.

In other embodiments, another factor may be utilized by the log₂estimator 330. In one example, the factor “32” in the log₂ estimator 330can be used to give a tradeoff between FLL settling time and filteringof noise from timing jitter in the reference frequency. In this example,the frequency may be tracked immediately in a single reference cycle.

The output of a bank of flip flops 336 is 16-bit frequency 344. Thefrequency 344 is sent into the input 338 of the subtractor block 334,and the output 332 of the estimator 330 is subtracted from the frequency344 on every cycle, resulting in a new value for the frequency 344. Thenew value for the frequency 344 is the D input into the bank offlip-flops 336, and this new value is updated on every referencefrequency cycle to get the frequency closer to the target.

In one embodiment, the target DCO frequency is 8,192 times faster thanthe reference frequency. In other embodiments, a differentmultiplication factor can be utilized (e.g., 2,048). The counter mayneed to have enough bits so that when the DCO 110 is running at itsmaximum frequency and the input signal is at the minimum allowedfrequency, the current and last counter values yield the number ofelapsed cycles without ambiguity (i.e., the counter must not repeat anystates between two successive reference clock edges). Although a 22-bitcounter is utilized in FIG. 3, a different number of bits may be used(e.g., 16 bits, 32 bits, etc.).

In the estimator block 330, the base-2 logarithm is estimated by apiecewise linear fit, of which one embodiment is shown graphically inFIG. 4. In some embodiments, first, the piecewise linear fit may beconstructed by creating breakpoints at all points on the x-axiscorresponding to (⅔)*2^(n), where n is an integer. Second, on theinterval xε((⅔)*2^(n), (⅔)*2^(n+1)) a line may be created, which passesthrough (x,y)=(2^(n),n) with slope equal to 1.5*2^(−n). In thisembodiment, n=0 corresponds to the line passing through (1,0), n=1corresponds to the line passing through (2,1), and so forth. Theequation for the line to the right of breakpoint “n” is:y=1.5*2^(−n)*x+n−1.5 (referred to as “Equation 3” herein), and,therefore, the left and right breakpoints can intersect at coordinates:(x,y)=((⅔)*2^(n), n−0.5) and ((⅔)*2^(n+1), n+0.5). As a result, thecurve is continuous over the range of the base-2 logarithm and passesthrough all the points whose y-coordinates are integers.

This approach may yield an estimation for the base-2 logarithm, whichmay be in error by a predetermined accuracy (e.g., at most 8.5%accuracy). In some embodiments, to create the breakpoints, the integerinput may be multiplied by 3 (e.g., by performing a binary addition ofthe input with a left-shifted version of itself), and the mostsignificant bit which is not set to zero may be identified in the result(e.g., using operation known as a “leading one detector”). This worksbecause numbers of the form (⅔)*2^(n), when multiplied by 3, result inexact powers of 2. The multiply-by-3 may be used directly in the familyof lines described in the Equation 3 (e.g., where a multiply by 1.5 is amultiply by 3 followed by a right shift) and all other operations aresimple shifts and additions.

This iterative frequency lock process can be understood as follows.First, a frequency error dF is assumed. The desired frequency is(8,192*Fref), and the actual DCO frequency is 8,192*Fref+dF. The 22-bitGray-code counter 108 will count (8,192*Fref+dF)/Fref=8,192+dF/Frefcycles. The logarithm estimator 330 will output 16log₂[1+dF/(8,192*Fref)].

The DCO 110 has an exponential frequency characteristic expressed byFdco=Fmin*2^(D/32). If the desired frequency is 8,192*Fref, the desireddigital code will satisfy the following equations:8,192*Fref=Fmin*2^(D/32) (referred to as “Equation 4” herein), and D=32log₂(8192*Fref/Fmin) (referred to as “Equation 5” herein). The actualDCO frequency with the error dF may imply the following digital code:Derr=32 log₂[(8,192*Fref+dF)/Fmin] (referred to as “Equation 6” herein).Then, (Derr−D) may be calculated in accordance with the followingequation: Derr−D=32 log₂[1+dF/(8,192*Fref)] (referred to as “Equation 7”herein).

The Equation 7 may give exactly twice the correction proposed above of16 log₂[1+dF/(8,192*Fref)]. The correction may be deliberatelyattenuated to allow the algorithm to filter some jitter noise, which maybe present in the reference signal 102. In one implementation, a factorof two may be chosen to optimize both tracking speed and noisefiltering. More attenuation of the digital word correction factor wouldcause the algorithm to settle more slowly, but would filter more noise.The full correction value of 32 log₂[1+dF/(8,192*Fref)] may be used formusic applications as it results in immediate frequency tracking withinone cycle of the input signal. In other embodiments, the tradeoffbetween settling speed and filtering may be optimized differently.

The output of the digital frequency iteration engine 106 may contain anynumber of fractional bits. As shown in FIG. 3, 8 fractional bits areretained and utilized to drive the second-order sigma-delta modulator112, which generates a sequence of digital frequency words D0, D1, D2through D255. In some embodiments, the output of the 8-bit sigma-deltamodulator 112 may be periodic with a period of at most 256 cycles. The“average” frequency of DCO 110 operation can be specified with 8 extrabits of accuracy beyond the existing 5 bits per octave. As a result, thefrequency granularity may be 13 bits per octave, 8,192 tones per octave,or almost 7 tones per musical cent (1 cent is 1/100 of a half step).Because this frequency granularity is so fine, the steps may beimperceptible and the FLL system 100 can track any given frequency onthe continuum between the minimum and maximum operating frequencies.

FIG. 5 illustrates an adaptive circuit 500 of the programmable divider114. As shown, the divider 114 receives the DCO output 124 and thefrequency 130 as input, and generates output signals CK75 120 and SCK116. In various embodiments, to generate the SCK clock 116, the divider114 divides the DCO output 124 by a certain number (e.g., by 2), anumber of times that would keep it in a tighter range. Since the integerpart of the desired DCO frequency 130 is known, the DCO clock down canbe divided by a variable power of two which is a function of the integerpart of the DCO frequency 130 such that frequency of the resultingoutput SCK 116 remains within a tighter range than that of the DCOitself (e.g., 100-200 kHz). The SCK 116 clock is then divided (e.g., by2048), producing the output CK75 120.

As shown in FIG. 5, the circuit 500 of the programmable divider 114includes an SCK generator 502 and a divide-by-2048 block 504. The SCKgenerator 502 is an adaptive sample clock generator, which receives theDCO output 124 and frequency 130 as an input, and generates the SCKsignal 116. The frequency 130 is the integer part of the desired DCOfrequency. The DCO output 124 may vary over a multi-decade range (e.g.,256 to 1 range from maximum to minimum frequency). The SCK clock 116 maybe within a tighter range (e.g., the SCK clock 116 varies in 2 to 1range instead of 256 to 1 range of the DCO output 124) than the DCOoutput 124 range.

The programmable divider 114 includes a divide-by-2048 counter 504,which converts the SCK signal 116 into the signal CK75 120. The outputsignal CK75 120 is a clock that varies between 50 Hz and 100 Hz.

In some embodiments, the programmable divider 114 may further include adivide-by-256 counter 506, and a programmable divider with two stages,with one stage dividing by 4, 5, or 6, and the other stage dividing by5, 6, 7, or 8. The counter 506 is a divide-by-256 counter, whichoperates on the DCO output 124. By selecting certain combinations of 4,5, or 6 and 5, 6, 7, or 8, the divider can create harmonies with theoriginal reference input. For example, if the first divider 508 isdividing by 4, and the second divider 510 is dividing by 8, the outputwill be in unison with the reference signal. In some embodiments, theprogrammable divider 114 does not include the counters 506, 508, and510.

FIG. 6A is a schematic 600 of the dropout detector 104 illustratingmeasuring of whether the reference frequency 102 goes away. The dropoutdetector 104 generates the dropout 126 based on the reference frequency102 and the CK75 signal 120 received from the output divider 114. Thegenerated dropout signal 126 is passed to the digital frequencyiteration engine 106. In some applications such as music synthesizers,the reference frequency (e.g., the reference frequency 102) may go away(e.g., if the music stops playing), and the dropout 126 would reflectthat.

FIG. 6B contains a state table 630 illustrating the state transitionsthat take place in the dropout detector 104 and a timing diagram 632illustrating some key signals present in the dropout detector 104. Thestate table 630 illustrates the states that the dropout detector 104goes through as the 3-bit Gray-code counter 602 is clocked. As the 3-bitGray-code counter 602 runs, only one bit changes in each of thetransitions. As shown in FIG. 6A, the CK75 signal 120 generated by theoutput divider 114 is passed to the 3-bit Gray-code counter 602 of the“dropout” detector 104. Each positive edge of the CK75 signal 120increments the 3-bit Gray code counter 602, which is reset whenever apositive edge is detected on the reference frequency 102 clock input viathe D flip-flops 604 and 606, an inverter gate 612, and a logic NANDgate 610.

In particular, the logic NAND gate 610 and the flip-flops 604 and 606generate a short negative pulse 618 that resets the 3-bit Gray-codecounter 602. First, the flip-flop 604 receives the reference frequency102 and the DCO output 124. If a reference clock edge occurs, thereference frequency 102 gets delayed by the DCO output 124 (the DCO isrunning faster). First, the reference frequency 102 goes through theflip-flop 604, which creates a first delay. Then, the flip-flop 606creates another delayed version.

If a positive edge occurs on the reference frequency 102, the 3-bitGray-code counter 602 is reset and the state machine 600 goes back tostate zero, and the 3-bit Gray-code counter 602 starts counting again.If the reference frequency 102 edges occur frequently enough, the 3-bitGray-code counter 602 never reaches the state of seven, and, as aresult, the dropout signal 126 stays low. When the 3-bit Gray-codecounter 602 reaches a count of seven, the state is seven, which drivesreset input of the flip-flop 608 low. As a result, this forces the “Q”of the flip-flop 608 low, and then the inverter 614 inverts the outputof the flip-flop 608, resulting in a high dropout 126.

As shown in FIG. 6B, the states table 630 illustrates the states thatthe 3-bit Gray-code counter 602 goes through in order from zero toseven, illustrating the property that only one bit is allowed to changeon a state transition. When the count is more than seven, the counteroutput remains in the 100 state.

In some implementations, when the 3-bit Gray-code counter 602 reachesthe final code 100, before a positive edge occurs on the reference clock102, the circuit 600 determines that the reference signal 102 has“dropped out.” The active-low reset input of the D flip-flop 608 isdriven low, forcing its output low, and the “dropout” signal 126 isdriven high. In some embodiments, this may take between 80 ms and 160ms, corresponding to 8 cycles of a 50-100 Hz signal. This time may beset sufficiently long such that any signal oscillating periodically at arate corresponding to the minimum possible dropout time (e.g., 80 ms) isguaranteed to be below the minimum frequency of the DCO 110. Given thatthe CK75 signal 120 and the reference clock signal 102 are asynchronousto each other, Gray-coding may be utilized for the counter 602 in thedropout detector 104 to prevent the dropout logic to inadvertentlytrigger because of counter bits passing temporarily through anout-of-order state.

When the dropout detector 104 detects that the reference signal 102 hasdropped out, the digital frequency iteration engine 106 is informed, sothat when the reference signal 102 returns, it will calculate the newperiod based on the next two reference edges rather than using a stalereference edge from before the reference signal 102 dropped out. Becausethe DCO control signal is digital, if the reference signal drops out itmay continue to oscillate at the last frequency locked indefinitely.

FIG. 6B illustrates a timing diagram 632 of signals 102, 120, 618, 620,and 622. As shown, the DCO signal 124 is faster than the referencefrequency signal 102. The signal 620 is a delayed version of thereference frequency 102, with the delay provided by the flip-flop 604.The signal 622 is a delayed version of the signal 620, with the delayprovided by the flip-flop 606. Accordingly, the signals 620 and 622 aredelayed versions of the reference frequency 102. The signal 618 isproduced by the logic NAND gate 610 and the inverter 612 using thesignals 620 and 622 as shown in FIG. 6A. In particular, the logic NANDgate 610 takes as input the signal 620 and output of the inverter 612(which in turn receives signal 622 as input), and produces the signal618, which is used to reset the counter 602.

FIG. 7 is a flow diagram of a process 700 for determining a newfrequency using a frequency generated by an oscillator and a referencefrequency. The process 700 can be implemented by the digital frequencyiteration engine 106, or by one or more other components of afrequency-locked loop circuit 100.

At block 702, a first frequency is received. The first frequency may bereceived from an oscillator that generated the first frequency. Theoscillator may be a digitally controlled oscillator. FIG. 2 provides anexample block diagram of an oscillator that generates the firstfrequency.

A reference frequency is received (block 704). The reference frequencymay be dynamic and change over a multi-decade range of frequencies. Anoscillator different from the oscillator that generated the firstfrequency may generate the reference frequency.

A number of first frequency cycles in one reference frequency cycle isdetermined (block 606). FIG. 3 illustrates one implementation ofdetermining the number of first frequency cycles that utilizes aGray-code counter, a Gray-to-binary converter, two banks of flip-flops,and a subtractor block. The output of the subtractor block (shown as theblock 314 in FIG. 3) provides the number of first frequency cycles inone reference frequency cycle.

At block 708, a dropout value associated with the reference frequency isreceived. The dropout value may be received from a dropout detector(e.g., the dropout detector 104). In one implementation, the dropoutvalue may be calculated by the dropout detector as shown in FIG. 6A.

A second frequency is determined (block 710) based on a predeterminedfrequency factor, the dropout value, the determined number of firstfrequency cycles, the first frequency, and the reference frequency. Inone embodiment, the second frequency may be calculated by performing apiecewise-linear logarithm calculation based on the predeterminedfrequency factor and the first input value determined by a multiplexor.The piecewise-linear logarithm calculation may involve estimating valueof 16 log₂ (the first input value/the predetermined frequency factor).

The predetermined frequency factor may provide target relationshipbetween the first frequency and the reference frequency. In someembodiments, a target frequency may be a result of multiplying thereference frequency by the predetermined frequency factor. In theseembodiments, it may be desirable to get the first frequency closer tothe target frequency. In one implementation, the predetermined frequencyfactor may have a value of 8,192.

Determining the second frequency may involve a multiplexor determining afirst input value based on the predetermined frequency factor, thedropout value, and the number of cycles, where the multiplexor receivesthe number of cycles and the predetermined frequency factor as inputs,and the dropout value as the selection input. When the dropout valueindicates that the signal of the reference frequency is not available,the multiplexor may assign the predetermined frequency factor to themultiplexor output, and if the dropout value indicates that the signalof the reference frequency is available, the multiplexor may assign thenumber of cycles to the multiplexor output.

Those skilled in the art would appreciate that the circuits describedherein may be realized using a variety of transistor types. Varioustransistor types can be used including bipolar junction transistors,junction field effect transistor, etc. The circuits described herein maybe fabricated with various IC process technologies (e.g., CMOS, silicongermanium, bipolar junction transistor, bipolar-CMOS, etc.).

The fast-locking frequency synthesizer described so far works very wellfor musical signals which don't possess strong harmonic components. Inparticular, it is assumed that the reference frequency 102 is a“well-behaved” sine or square wave. In practice, this referencefrequency is generated by passing a musical signal, for example from amicrophone or electric guitar, through a low-pass filter and then azero-crossing detector. But most practical musical signals containharmonic tones at twice, three times (and higher) the fundamentalfrequency which can be as much as 10 dB stronger than the fundamentaltone. These harmonics can create “false zero crossings” which willgenerate undesired edges on reference clock 102, ultimately causing thefrequency synthesizer to lock to one of the harmonics instead of thefundamental.

In order to mitigate synthesizer locking to harmonics of thefundamental, a low-pass filter is desired which can be self-tuned tofilter out the harmonics well enough that they will not create thesefalse zero crossings and undesired edges on reference clock 102.

In any synthesizer which tracks the fundamental input frequency of amusical signal from a voice or any instrument, including but not limitedto electric guitar, bass guitar, brass, woodwinds, bowed strings,percussion, it is of crucial importance to correctly identify thefundamental frequency in that signal. Often the second, third, or higherharmonics are larger in amplitude than the fundamental, which poses aserious difficulty to isolating the fundamental. Because the “musicallyuseful” frequency range of all instruments covers about 8 octaves, fixedfilters are out of the question. The proper filter for isolating thefundamental component of the signal from an arbitrary musical voice mustchange dynamically with the input frequency.

The fast-locking frequency synthesizer (“FLL”) described above containsa digitally-controlled oscillator (“DCO”) 110 whose frequency iscontrolled by a 16-bit frequency word (130 and 132). This 16-bitfrequency word is converted to an 8-bit frequency word 136 using astandard second-order sigma-delta modulator as follows: The 8-bitfractional part of the frequency word 132 is presented at the input ofthe sigma-delta modulator, which generates a 2-bit sequence whoseaverage value over time equals the fractional part of the frequency.This 2-bit sequence is added to the 8-bit integer part to generate thefinal 8-bit frequency word 136 that drives the DCO itself. So the DCOfrequency is actually changing slightly on every cycle with the resultthat the average frequency is as desired.

The present invention, illustrated in FIG. 8, adds an 8-bitdigital-to-analog converter 111 whose input is driven by this samesigma-delta-modulated 8-bit frequency word 136. Recall that thefrequency vs. digital code obeys an exponential characteristicFdco=Fmin*2^(D/32), where D represents the 8-bit frequency control word136. This means that when this 8-bit frequency control word is convertedto an analog voltage using a digital-to-analog converter, the resultinganalog voltage will be a representation of the detected input frequency,where the voltage is proportional to the logarithm of frequency.Appropriate scaling can give a voltage which changes by one volt forevery 2× increase in frequency. Such a scaling (1v/octave) is verycommon in electronic music applications, for example modular andsemi-modular synthesizers. We call this 1v/octave voltage correspondingto the input frequency “pitch CV out.”

It is very common for 1v/octave voltage signal to be used as a controlvoltage (“CV”) input for other functions common in music synthesizers.Such control voltages can influence the frequency of voltage-controlledoscillators (VCOs) or the cutoff frequency of voltage-controlled filters(VCFs), to name some common examples. The present invention adds avoltage-controlled low-pass filter with high frequency shelf (“inputfilter”) 105 in front of the fast-tracking frequency synthesizer toeliminate harmonics present in the input music signal which might causeerrors in the frequency detection apparatus as described above. When thefrequency CV input of this input filter is varied, the filter cutofffrequency is designed to vary with the same 1v/octave characteristicthat is provided in the pitch CV out described above. In addition, thisinput filter features a high-frequency shelf, implemented by attenuatingthe input by a factor “a” (equal to 1/10 in the case of 20 dB shelfattenuation) using attenuator 113 and adding the resulting signal backinto the filter output. This high-frequency shelf limits the filterattenuation to a certain maximum attenuation for high frequencies. Thekey of the invention is to couple the 1v/octave pitch CV out 107 backinto the frequency CV input of the input filter so that the filterfavors forcing the synth to lock to the fundamental component in theinput musical signal, even when there are large harmonic componentspresent in this input.

The input filter must fulfill a few basic requirements. (1) When thefrequency is locked to a particular frequency f₀ and the pitch CV outhas settled to a constant value represented by f₀, it is convenient todemand that the gain of the filter at f₀ should be 0 dB. (2) If thefilter is normalized in this way, it should have at least 14 dB gain atfrequencies less than f₀/2 and at least 14 dB attenuation at frequencieshigher than 2f₀. (3) The high frequency shelf must be present so thatthe attenuation will not exceed about 20 dB in the stopband because whena low note is played and the filter tracks to the low note, it isdesired for the filter to still have enough gain at high frequencies todetect if the next note played happens to be a high note. The 14 dB gainand attenuation requirements, as well as 20 dB stopband attenuationrequirement, are not intended to restrict the invention in any way.Equivalent embodiments that provide more or less attenuation are alsoconsidered to be within the scope of this invention.

The input filter requirements can be understood as follows: If thefast-locking frequency synthesizer happens to lock to the second (orhigher) harmonic in a music signal, the filter guarantees that thefundamental will have at least 14 dB more gain than the harmonic towhich the synth would like to lock. This should cause the synth toprefer the fundamental and lock to the fundamental. When this happensand the filter tunes to the correct frequency, the second and higherharmonics will still be attenuated by at least 14 dB relative to thefundamental frequency and the frequency should remain locked to thefundamental.

Voltage-controlled filter design is well known in the art, therefore thepresent invention will only describe the filter in general terms. In thepresent invention, voltage-controlled low-pass filter 105 is expanded inFIG. 9. The 1v/octave Pitch CV signal 203 is applied to an exponentialvoltage to current convertor 205. The output current of this blockdoubles for every 1v increase in the input voltage. The resultingcurrent is then used to control the cutoff frequency inCurrent-Controlled Filter 209. To meet the requirements discussed above,the present invention uses a 4-pole filter consisting of a cascade oftwo 2-pole biquad sections. Each biquad has DC gain of 2.4 and thequality factor (“Q”) of each biquad is tuned for maximal flatness. Toachieve the stopband 20 dB attenuation, also known as the high-frequencyshelf, the unfiltered audio signal is attenuated by a factor of 1/10 andthen mixed back into the filter output using a voltage divider withappropriately-scaled resistors.

FIG. 10 shows the magnitude transfer function of the filter used in thisembodiment of the invention. Note that the frequency is scaled hererelative to any particular frequency f₀ that the synthesizer can lockto. When the input frequency changes and the pitch CV output changesaccordingly, the filter scales exactly like FIG. 10 to keep the gain atthe locked frequency f₀ exactly 0 dB, the gains at frequencies less thanf₀/2 higher than 14 dB and the attenuation at frequencies higher than2f₀ higher than 14 dB.

FIG. 11 shows the group delay of the filter used in this embodiment ofthe invention. Note that the units of group delay are in cycles of thelocked frequency f₀. This dimensionless quantity was chosen to simplifythe stability analysis, discussed below.

Because the input filter influences the waveform presented at the inputto the fast-locking frequency synthesizer, the pitch CV out depends onthe detected frequency (which depends on the aforementioned inputwaveform, and the input filter is influenced by the pitch CV out, it isclear that the invention can be considered a feedback system. As withall feedback systems, it is important to be able to guarantee stability.There are two free parameters in this system which will impactstability: (1) The group delay D of the input filter; (2) The trackingspeed factor A of the fast-locking frequency synthesizer. A is therelative factor compared to 32 in the log₂ estimator 330; in otherwords, if the log₂ estimator 330 uses 32 as the factor, A=1 and if thelog₂ estimator 330 uses 16 as the factor, A=½. Group delay of the filteris important because when the filter cutoff frequency is adjusted, thephase of the filter output will move by an amount corresponding to thisgroup delay.

FIG. 12 illustrates a simplified block diagram and difference equationsof the feedback system for stability analysis. This is a small signalmodel, where all quantities are considered small perturbations fromtheir ideal values. The input to the system φ_(in) is an added phaseperturbation at the input of the frequency synthesizer, which is onlyintroduced to see whether the system is susceptible to noise oroscillation at any frequency. The system is second-order and the endresult is quite simple: According to Equation 12, to guarantee stabilitythe product of group delay D and log₂ estimator factor A must be lessthan one. For the particular filter used in this invention, the groupdelay can be larger than one for some frequencies. This means that it isbest to avoid the log₂ estimator factor of one to mitigate the risk ofoscillation.

The filter proposed in this invention is just one of many filters thatcould be used. Other filters should be considered within the scope ofthe invention. In particular, a filter with more poles could be used toachieve even more attenuation of the second and higher harmonics ifnecessary. Other filters might have smaller (or larger) group delay andwould therefore impose different constraints on the log₂ estimatorfactor to guarantee stability.

Those skilled in the art would appreciate that the circuits describedherein may be realized using a variety of transistor types. Varioustransistor types can be used including bipolar junction transistors,junction field effect transistor, etc. The circuits described herein maybe fabricated with various IC process technologies (e.g., CMOS, silicongermanium, bipolar junction transistor, bipolar-CMOS, etc.).

The previous description of the disclosure is provided to enable anyperson skilled in the art to make or use the disclosure. Variousmodifications to the disclosure will be readily apparent to thoseskilled in the art, and the generic principles defined herein may beapplied to other variations without departing from the spirit or scopeof the disclosure. Thus, the disclosure is not intended to be limited tothe examples described herein but is to be accorded the widest scopeconsistent with the principles and novel features disclosed herein. Forexample, many circuits are possible for implementing the digitalfrequency iteration engine 106, the dropout detector 104, the DCO 110,the output divider 114, the sigma-delta modulator 112, and the FLLcircuit 100. Further, for example, many circuits are possible forimplementing the voltage-controlled low-pass filter 105, and thedigital-to-analog converter 111. These systems may be implemented withanalog electronics, digital logic, software executing on a processor, orany combination of these or other techniques.

What is claimed is:
 1. A method for generating frequencies in a musicsynthesizer, the method comprising: receiving a first frequencygenerated by an oscillator; receiving a reference frequency that hasbeen passed through an auto-tuning low-pass filter; determining a numberof first frequency cycles in one reference frequency cycle; anddetermining a second frequency based on a predetermined frequencymultiplication factor, the determined number of first frequency cycles,the first frequency, and the reference frequency, wherein thepredetermined multiplication factor provides target relationship betweenthe first frequency and the reference frequency, wherein determining thesecond frequency comprises determining a first input value based on thepredetermined frequency multiplication factor, a dropout value, and thenumber of first frequency cycles; and performing a piecewise-linearlogarithm calculation based on the predetermined frequencymultiplication factor and the first input value.
 2. The method accordingto claim 1 wherein the auto-tuning low-pass filter is avoltage-controlled filter with an exponential relationship between aninput voltage and a filter cutoff frequency.
 3. The method according toclaim 2 wherein the auto-tuning low-pass filter has a high frequencyshelf.
 4. A frequency-locked loop circuit comprising: a digitallycontrolled oscillator con figured to generate a first frequency; anauto-tuning low-pass filter that receives an input signal and outputs areference frequency, a dropout detector configured to receive thereference frequency, and generate a dropout value; and a digitalfrequency iteration engine comprising: a first circuit configured toreceive the first frequency and the reference frequency, and generate anumber of first frequency cycles in one reference frequency cycle; and asecond circuit configured to receive the number of first frequencycycles, and generate a second frequency based on a predeterminedfrequency multiplication factor, the dropout value, the determinednumber of first frequency cycles, the first frequency, and the referencefrequency, wherein the predetermined frequency multiplication factorprovides a target relationship between the first frequency and thereference frequency, and wherein a divider is configured to receive thefirst frequency from the digitally controlled oscillator, generate athird frequency, and transmit the third frequency to the dropoutdetector.
 5. The frequency-locked loop circuit according to claim 4wherein the auto-tuning low-pass filter is a voltage-controlled filterwith an exponential relationship between an input voltage and a filtercutoff frequency.
 6. The frequency-locked loop circuit according toclaim 5 wherein the auto-tuning low-pass filter has a high frequencyshelf.
 7. A frequency-locked loop circuit comprising: an auto-tuninglow-pass filter that receives an input signal and outputs a referencefrequency, a digitally controlled oscillator configured to generate afirst frequency; and a digital frequency iteration engine comprising: afirst circuit configured to receive the first frequency and thereference frequency, and generate a number of first frequency cycles inone reference frequency cycle; and a second circuit con figured toreceive the number of first frequency cycles, and generate a secondfrequency based on a predetermined frequency multiplication factor, thedetermined number of first frequency cycles, the first frequency, andthe reference frequency, wherein the predetermined frequencymultiplication factor provides a target relationship between the firstfrequency and the reference frequency, and a counter con figured toreceive the reference frequency and the first frequency, the countercoupled to the digital frequency iteration engine.
 8. Thefrequency-locked loop circuit according to claim 7 wherein theauto-tuning low-pass filter is a voltage-controlled filter with anexponential relationship between an input voltage and a filter cutofffrequency.
 9. The frequency-locked loop circuit according to claim 8wherein the auto-tuning low-pass filter has a high frequency shelf. 10.A frequency synthesizer comprising: a frequency-locked loop circuitcomprising: a digitally controlled oscillator configured to generate afirst frequency; an auto-tuning low-pass filter that receives an inputsignal and outputs a reference frequency, a dropout detector configuredto receive the reference frequency and a first frequency, and generate adropout value; and a digital frequency iteration engine comprising: afirst circuit comprising a Gray-code counter, a Gray-to-binaryconverter, a first plurality of flip-flops, the first circuit configuredto receive the first frequency and a reference frequency, and generate anumber of first frequency cycles in one reference frequency cycle; and asecond circuit comprising a multiplexor, a second plurality offlip-flops, and an estimation module, the second circuit configured toreceive the number of first frequency cycles, and generate a secondfrequency based on a predetermined frequency multiplication factor, thedropout value, the determined number of first frequency cycles, thefirst frequency, and the reference frequency, wherein the predeterminedfrequency multiplication factor provides a target relationship betweenthe first frequency and the reference frequency.
 11. Thefrequency-locked loop circuit according to claim 10 wherein theauto-tuning low-pass filter is a voltage-controlled filter with anexponential relationship between an input voltage and a filter cutofffrequency.
 12. The frequency-locked loop circuit according to claim 11wherein the auto-tuning low-pass filter has a high frequency shelf.